Discusses: (1) different types of learning (concepts, properties, facts, procedures, algorithms, skills, and problem solving); (2) types of learning behaviors; and (3) types of representational models, considering concreteness, meaningfulness, and manipulation (active manipulation, passive manipulation, and nonmanipulation). (JN)

Use of manipulatives is neither a sufficient nor a necessary condition for meaningful learning. Provides some incidents in support of the argument. Lists 14 references. (YP)

Discusses planning lessons for the learning disabled student. Defines four deficits: (1) visual-processing deficit; (2) auditory-processing deficit; (3) kinesthetic deficit; and (4) reasoning disorders. Describes strategies for each of the four deficits. (YP)

A description of a planet in the shape of a cube where everything was built from squares and parts of squares is presented. The story is used as a background for several paper folding exercises that explore several geometric shapes. Solutions to the problems stated are included. (MP)

Some activities involving distances and diameters in the solar system are discussed. (MP)

Article is based on the keynote address of the 1987 annual meeting of the National Council of Teachers of Mathematics. Suggests that George Polya left a legacy which has not only touched knowledge and abilities in mathematics and problem solving but also had significant effects on thoughts about teaching. (PK)

Discussed are different aspects of interviewing that will help a teacher to learn weaknesses and strengths of students' mathematical thinking. Information learned from the students can have a dramatic effect on what is taught, when it is taught, how it is taught, and how a child's progress is evaluated. (RH)

Suggests that teachers use "warm-up" activities to introduce their lessons. Examples of 25 such activities are presented. All of the activities can be modified to meet the needs of particular students. (JN)

Describes two sets of activities designed to stimulate thinking skills and to bring some topological aspects into the mathematics curriculum. One set explores Mobius strips; the other set deals with tori. The activities are suitable for students in fourth through eighth grades. (JN)

Third- and fourth-grade students were introduced to palindromes (numbers that can be read the same both forward and backward). The types of problems that they generated, investigated, and solved are presented. (JN)

Presents activities designed to help children understand the notion of a sample in a homogeneous group, a concept essential to understanding "R times E" problems. Underscores the importance of children's understanding the situation in a problem so that they can solve it. (JN)

The number charts described in this article have been used successfully with elementary students as young as first graders to teach the concepts of even and odd numbers. Students construct charts and then answer a series of questions about the patterns that they observe. (RH)

Describes activities designed as self-checking tasks involving practice with whole number operations. Materials consist of a set of boards partitioned into 36 squares; sets of 36 sentence/picture cards correspond with each board. A correct sentence or picture is then formed as students correctly perform the necessary mathematical operations. (JN)

First-grade children mastered 72 of 100 addition facts by the middle of the grade, with mastery being defined as a two-second response to a given addition fact. A sequence of activities is presented that serves as an outline of the approach taken. (JN)

Presents a problem-solving activity in which students first guess and then check their answer. Also presents an activity to help students develop skill in understanding the question in a problem and a suggestion to help develop a classroom climate conducive to problem-solving. (JN)